Transferring message history to new iPhone (w/o backup)

Short question: I just bought a new iPhone and am can't figure out how to transfer my message history onto the new device from Messages.app on my Mac.

Long story: My old iPhone had something corrupted in the OS so I didn't want to do a backup/recovery approach to the migration through iCloud to prevent the problem from coming along with the data.

I've setup new one using the New iPhone workflow and have connected to iCloud so all my contacts, calendar info, etc., are now on the new phone.

My problem is that the my (text) message history didn't make it over to the new phone. It's still in the Messages app on my Mac but I need guidance on how to make it also show on the phone.

In case you're curious, the old phone has been wiped and traded-in.

Ideas? Suggestions? All help appreciated.

Thanks,

Steve